Claims reserving in the hierarchical generalized linear model framework

Gigante, Patrizia; Picech, Liviana; Sigalotti, L.

doi:10.1016/j.insmatheco.2013.02.006

Cited by 13 publications

(18 citation statements)

References 22 publications

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“…Relaxation of this assumption may lead to hierarchical generalized linear models (HGLM) as they are used, for instance, in Gigante et al . (2012). However, many of the analytical properties get lost in these more complex models and either simulations or approximations need to be used.The model can be generalized to sub-portfolios n all having different dimensions I and J .…”

Section: Model Assumptionsmentioning

confidence: 99%

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Dependence modelling in multivariate claims run-off triangles

2012

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A central issue in claims reserving is the modelling of appropriate dependence structures. Most classical models cannot cope with this task. We define a multivariate log-normal model that allows to model both, dependence between different sub-portfolios and dependence within sub-portfolios such as claims inflation. In this model we derive closed form solutions for claims reserves and the corresponding prediction uncertainty.

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Section: Model Assumptionsmentioning

confidence: 99%

“…(2012) can be interpreted as a hierarchical structure which leads to a new interesting family of models related to hierarchical generalized linear models (HGLM), see Gigante et al . (2012).…”

Section: Introductionmentioning

confidence: 99%

Dependence modelling in multivariate claims run-off triangles

2012

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“…However, this model will in general not allow for closed form solutions, see Section 3.3.3 in McNeil et al [13]. Other interesting extensions are so-called hierarchical generalized linear models (which also need to be solved numerically), see Gigante et al [4].…”

Section: Remarkmentioning

confidence: 99%

“…To study more general models one could further consider hierarchical generalized linear models, see e.g. Lee et al [12] and Gigante et al [4] (see also Remarks 1) or approaches from classical linear credibility theory, see Bühlmann and Gisler [1]. The correlation parameter q was not calibrated from data.…”

Section: Limitations and Possible Extensionsmentioning

confidence: 99%

Modeling accounting year dependence in runoff triangles

Salzmann

Wüthrich

2012

Eur. Actuar. J.

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Typically, non-life insurance claims data is studied in claims development triangles which display the two time axes accident years and development years. Most stochastic claims reserving models assume independence between different accident years. Therefore, such models fail to model claims inflation appropriately, because claims inflation acts on all accident years simultaneously. We introduce a Bayes chain ladder reserving model which enables us to model claims inflation. In this model we derive analytical formulas for the posterior distribution, the claims reserves and their prediction uncertainty. Keywords Accounting year effects modeling Á Claims inflation Á Bayes chain ladder model Á Multivariate dependence modeling Á General insurance liabilities Á Outstanding loss liabilities Á Claims reserving Á Loss development

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“…Such models are called Hierarchical Generalized Linear Models (HGLMs). The use of HGLMs in loss reserving has been considered in Gigante et al (2013a) and Gigante et al (2013b).…”

Section: Introductionmentioning

confidence: 99%

A Mixture Model for Payments and Payment Numbers in Claims Reserving

Gigante¹,

Picech

Sigalotti³

2016

ASTIN Bull.

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We consider a Tweedie's compound Poisson regression model with fixed and random effects, to describe the payment numbers and the incremental payments, jointly, in claims reserving. The parameter estimates are obtained within the framework of hierarchical generalized linear models, by applying the h-likelihood approach. Regression structures are allowed for the means and also for the dispersions. Predictions and prediction errors of the claims reserves are evaluated. Through the parameters of the distributions of the random effects, some external information (e.g. a development pattern of industry wide-data) can be incorporated into the model. A numerical example shows the impact of external data on the reserve and prediction error evaluations

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Claims reserving in the hierarchical generalized linear model framework

Cited by 13 publications

References 22 publications

Dependence modelling in multivariate claims run-off triangles

Dependence modelling in multivariate claims run-off triangles

Modeling accounting year dependence in runoff triangles

A Mixture Model for Payments and Payment Numbers in Claims Reserving

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